Problem with linking Objects to Bone
First thing, you should lower down the Subsurf View value of all your objects to 2 because at 5 it's hard to work.

Now, about your problem, it's because your eyes, eyebrows and eyelids are separate objects, and you didn't parent them With Automatic Weight but directly to armature as a simple parent: as you can see, if you select them, enter in Edit mode, and see what are their vertex groups in the Properties panel > Data > Vertex Groups, there's only Armature (meaning the armature object on its whole will move these objects, but not the bones within this armature, i.e. like a basic parentage from an object to another).

So first select eyes, eyebrows and eyelids, join them to the whole body with ctrlJ, go back in the vertex groups list of the whole body and delete this Armature group. Now assign all these new vertices to the group called "head". It should work (well, still some corrections to make in Weight Paint mode so that the neck bone doesn't affect the head mesh).

Hurray and Happy New Year !!!!